Lamplighter groups, median spaces and Hilbertian geometry
Copyright policy )Lamplighter groups, median spaces and Hilbertian geometry
AbstractFrom any two median spaces $X$ and $Y$, we construct a new median space $X \circledast Y$, referred to as the diadem product of $X$ and $Y$, and we show that this construction is compatible with wreath products in the following sense: given two finitely generated groups $G,\,H$ and two (equivariant) coarse embeddings into median spaces $X,\,Y$, there exist a(n equivariant) coarse embedding $G\wr H \to X \circledast Y$. The construction offers a unified point of view on various questions related to the Hilbertian geometry of wreath products of groups.
Extensions, wreath products, and other compositions of groups, median spaces, Kazhdan property (T), Metric Geometry (math.MG), Group Theory (math.GR), compression, Haagerup property, Hyperbolic groups and nonpositively curved groups, CAT(0) cube complexes, Mathematics - Metric Geometry, wreath products, FOS: Mathematics, 20F65, 20F67, 43A15, Geometric group theory, Mathematics - Group Theory
Extensions, wreath products, and other compositions of groups, median spaces, Kazhdan property (T), Metric Geometry (math.MG), Group Theory (math.GR), compression, Haagerup property, Hyperbolic groups and nonpositively curved groups, CAT(0) cube complexes, Mathematics - Metric Geometry, wreath products, FOS: Mathematics, 20F65, 20F67, 43A15, Geometric group theory, Mathematics - Group Theory
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